help-27

[twin quarry]

i havent even been taught to do this tbh

she just gave the hw

so what i do

wdym by approximate

like should I round it

to

2

decimals

ok

both of them?

sooooooooo

what should I do sir

nope

its just homework

ok

which rounded x

oh ok

so sub the first one

x = blah y = blah

then do the 2nd one?

[woven radish]

Lambda

[twin quarry]

so where x = 0.90

Y = 7.70?

on the first one

it says it is incorrect

idk

oh

x=0.895644

yeah

I said 0.90

[woven radish]

Lambda

Lambda

Lambda

[twin quarry]

so what should I do

[woven radish]

Lambda

[twin quarry]

yeah

i put

b = 2

[meager jackal]

After simplified u will get$\frac{2 \pm \sqrt{84}}{8}$

[woven radish]

Noone

[twin quarry]

for the

plus or minus

which one do i put

[meager jackal]

Yes

[twin quarry]

oh

so

i do one with

• and one with -

seperately?

[meager jackal]

Yes

And u will get 2 answer

[twin quarry]

ok

[meager jackal]

Then round off to two decimal places

[twin quarry]

1.395643924

-0.8956439237

these were the 2 answers

what should I do next

[meager jackal]

Round off to 2 d.c.

D.p.

I mean

[twin quarry]

1.40

-0.90

[meager jackal]

Yes

[twin quarry]

then

ok

so

y= 3(1.40) + 5

?

9.2

do

I go with the rounded or no

i put

x = 1.40

y = 9.20

ayyy

after 4 hours I get the mark

nah it was right

ima do the 2nd one

ok I got right

thanks @reef tendon @meager jackal

[meager jackal]

Ur wlc

[twin quarry]

bet

.close

[devout snow]

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[golden eagle]

idk how to go

[zenith jacinth]

what do you know about an hermitian matrix ?

[golden eagle]

A = A^T*

[stone stump]

plug that in. simplify

you'll get (number) = (number)^*, so the number has to be real

[golden eagle]

how will the simplifying go

x**Ax = x*(A^T*)x

now what

[zenith jacinth]

hmm basically, we need to prove that :
$(X* AX)* = X*AX$ if im not wrong

Wow

[stone stump]

use \overline

[zenith jacinth]

ok

$\overline{\overline{X} AX} = \overline{X} AX$

[woven radish]

Ｈｅｒｅｌｓ

[zenith jacinth]

since A is hermitian, we plug transpose of A* in it and we'll see what happen

$\overline{\overline{X} (\overline{A})^T X}$

damn..

[woven radish]

Ｈｅｒｅｌｓ

[zenith jacinth]

which is equal to :
$X \overline{(\overline{A})^T} \overline{X}$

[woven radish]

Ｈｅｒｅｌｓ

[zenith jacinth]

now how to calculate that thing in the middle

[golden eagle]

yes

i think i don't get it yet

[golden eagle]

what happened

[zenith jacinth]

this is what we want to prove

[golden eagle]

is this a property?

[zenith jacinth]

well yes, if a scalar is real,his conjugate is himself

[golden eagle]

i think i am so lost

[zenith jacinth]

huh

5* = 5

[golden eagle]

what does a scalar have to do here

[zenith jacinth]

because X* AX is a scalar

[golden eagle]

and how did i know that

[zenith jacinth]

well X is a vector and A a matrix

[golden eagle]

and ?

i think i am missing something here

[zenith jacinth]

$\begin{pmatrix} x^{} & y^{} \end{pmatrix} \begin{pmatrix} a & b \ c & d \end{pmatrix} \begin{pmatrix} x \ y \end{pmatrix}$

hmm the first one should be transpose to return a scalar, and we cant multiply vectors

[woven radish]

Ｈｅｒｅｌｓ

[devout snow]

@golden eagle Has your question been resolved?

[golden eagle]

i think i will search more and try to make sure that i understand everything that i need to understand this.
thank you for your help

.close

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[oak latch]

yo

[devout snow]

Please don't occupy multiple help channels.

[oak latch]

.close

[devout snow]

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[oak latch]

.reopen

[devout snow]

✅

[oak latch]

yo

can somone explain this?

https://i.imgur.com/7G4fgf6.png

[devout snow]

@oak latch Has your question been resolved?

[oak latch]

.close

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[grand edge]

Hey there, just wondering how I can calculate the bias of a list of estimators

[grand edge]

What ive currently done is the sum of abs(real value-estimate value i) and then dividied by the no.estimators

Im not really sure about the absolute value though, like lets say if the value I wanted is 0, and I estimate 0.2 and -0.2, the mean of those is 0 but am I right in saying the bias is still 0.2

[devout snow]

@grand edge Has your question been resolved?

[devout snow]

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[sly gorge]

.close

[devout snow]

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[sly gorge]

I have like 5 questions to ask

what is the point of symmetry on this graph

what is the endpoint of the graph

Which is not a valid restriction on the domain

what are the 3 right transformations for this graph

what are all the correct transformations for this graph

[devout snow]

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[gleaming socket]

where is your issue

[regal vector]

The graph

How do i draw the graph like what do i use

[karmic abyss]

You've solved the equation for t when h=0, and found out the overall time ∆t for the ball's flight, correct?

[regal vector]

What

Do u mean a

I tried to make my own table where t is 0,1,2 and m is 0,8,8

But the table in the book in the table only goes till 2 for t and m goes till 5 so its kinda impossible

[karmic abyss]

Could you clarify what you mean by this?

[regal vector]

I meant graph part

[karmic abyss]

Ah

We actually don't need to put (0,0) at the center of the page; that's just a convention that's used when a function is most interesting around the origin

But for this function, we care only when 0 ≤ t ≤ 4, so we should probably have the origin towards the left side, since we don't care about negative values of t in this case.

[regal vector]

What

So how do i

[karmic abyss]

Here's an example of what I mean

The main X and Y axes can be drawn anywhere on the page; you just need to appropriately plot the graph for those axes

It's not a requirement that (0,0) is at the center of the page

[regal vector]

So where do i start it

[karmic abyss]

Well, what is the range of t?

[regal vector]

Range?

Would it be easier if i use graph paper

[karmic abyss]

Yeah most likely; I just don't have any on hand

[regal vector]

I have an a3 graph paper book is that an overkill

[karmic abyss]

What is the minimum value of t and the maximum value of t that should definitely be on that graph?

[regal vector]

This maybe

[karmic abyss]

you should still be able to do it in the workbook; there actually is enough space for it

[karmic abyss]

Yep, that's good, though you should also include when t=3, since we care about its entire flight path

[regal vector]

Ok

[karmic abyss]

And another consideration: on the interval from 0 to 3 (the interval we're tracking), is h(t) ever negative?

or to make it more general, what is the smallest value that h(t) should be, when we plug in numbers between 0 and 3

[regal vector]

What

[karmic abyss]

Ah, sorry for not explaining where I'm going with this. We positioned the t/x axis to include everything we want, but we should still position the h(t)/y axis to include everything we wanted to

your table shows that h(t) can definitely be 0 and 8, so we should position the graph so that both of those values are included

[regal vector]

One sec

Something like this

?

[karmic abyss]

It seems you've adjusted the scale (how far apart the numbers are) and left the origin (the point (0,0)) in the center of the page.

[regal vector]

Wat

[karmic abyss]

Recall that the problem asked for a specific scale, but didn't tell you where to put (0,0) on the page

Notice how you have the part where t < 0 still on the page

But we don't really need to plot anything on that part for the question, since the ball can't go below the ground

[regal vector]

Im confused

[karmic abyss]

My bad

So do you see how 0,0 is in the center of the page?

[regal vector]

Ye

[karmic abyss]

Recall that the question asked us to graph the portion of the graph where the ball was in flight

When the time is less than 0, i.e. before you throw the ball, has the ball taken flight?

[regal vector]

No

[karmic abyss]

Yep, exactly

So in that case, we can position the point (0,0) of the graph such that there's no (or a very small) part of the graph where t < 0

Since we don't care about it for the problem

Does that make sense?

[regal vector]

Kinda

I need to make m section

2 cm for one

N t section 4 cm for one

[karmic abyss]

Yep

Yea

So, if we position the origin somewhere on the left side of the page, can we fit all three seconds (the time the ball is in the air) on the page when the interval is 4cm/1 second

[regal vector]

Does it make a diff if u start it ata left?

[karmic abyss]

Not unless you need negative values, which we don't

How a graph is positioned is really more of an aesthetic/practical thing, it shouldn't impact our graph

[regal vector]

Wr dont need the negative value for this?

[karmic abyss]

We don't need negative values of t, because, as you said, the ball isn't flying before it's thrown

[regal vector]

Ok

[karmic abyss]

It does end up being the case that we also don't need the vertical axis to ever be negative, since something thrown shouldn't ever be below the ground

Speaking of, we should take a similar process for the vertical part.

As per your table, you need to include both 0 and 8 on the graph, so we should position the origin so that both of those heights are present.

If it helps with finding positions, I claim that the function h(t) is never less than 0 between t=0 and t=3, and I encourage you to double check this

[regal vector]

So something like this

[regal vector]

I double checked with the answer key in the back

[devout snow]

@regal vector Has your question been resolved?

[devout snow]

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[sage socket]

Can someone assist me with this question? What exactly is it asking? My book doesn't provide an example...

[random temple]

if x is in [0,2pi), when is f(x)=0?

[sage socket]

oh!

okay

and to be clear, f(x)= cos x right?

[random temple]

yes

[olive atlas]

Sure

[sage socket]

okay sick

that's not hard

I could just use the unit circle

[random temple]

yeah do that

[sage socket]

hmmm

cos x can be 0 at pi/2 and 3pi / 2

[sage socket]

I'm just looking for the output right?

but how do I know what quadrant to look at

[random temple]

all quadrants

[sage socket]

oh boy

[random temple]

but you got the answer already

this is correct

[sage socket]

oh

it can be either?

okay

[random temple]

yeah

[sage socket]

or both

rather

[random temple]

yeah both

[sage socket]

now

what would you do if you didn't have the uint circle

[random temple]

why would you not have the unit circle

[sage socket]

cause it looks like it wasn't me to solve the function at 0

[random temple]

unit circle is the definition of cos

you kinda need it

[sage socket]

hmmm

is there a way to do it without it?

[random temple]

I guess you could graph the function in cartesian plane

but how would you know where the solutions are without the unit circle

[sage socket]

I don't know

I recall my professor using triangles

for one problem

I did ask him about his method, he told me to just use the unit circle lol.,..

maybe I'll just stick with it

[sage socket]

so , does it matter if I use degrees or radians here?

[random temple]

well you should use radians

because f(x)=cos(x) is in radians unless otherwise specified

[sage socket]

oh right

cause cosine is a function for an angle right?

[devout snow]

@sage socket Has your question been resolved?

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[junior gale]

how do I find the derivative of this?

[prime egret]

Do it a few times and find a pattern

[junior gale]

after that?

i did it three times

[prime egret]

Do you spot something

[junior gale]

yeah when i take the odd derivative its negative and even its positve

and the exponent gets multiplied by itself by how many times the derivative is

how would i show my answer?

like is x now 2016 and I have to find the derivative of that?

cuz it will be 0

and the answer key says its 2016!

so i am confused

[winter patrol]

show your first 3 derivatives

of f(x)

[junior gale]

here

[prime egret]

2016 —> 2016x2015 —>2016x2015x2014 do you see where this is going

[junior gale]

yes it multiples by (2016-n)!

n being the derivative

[prime egret]

Not quite if it’s multiplied by that the first derivative would be multiplied by 2015!

Which is 2015x2014x2013x…x1

[junior gale]

so what would it be then?

[prime egret]

Do you just want me to tell you?

[junior gale]

i just dont know thats the issue

like how would i show the pattern

[prime egret]

Well first let’s account for the sign

It alternates between negative and positive

[junior gale]

the sign would be postive

because its a even deriavitew

[prime egret]

Yeah okay but in general the nth derivative will have the sign (-1)^n

Yeah?

[junior gale]

ok?

[prime egret]

I’m trying to just conjecture a general solution for the nth derivative here

[junior gale]

ok

[prime egret]

So we have $(-1)^n \cdot …$

[woven radish]

Pure

[prime egret]

Now for the power of (1-x)

[junior gale]

ok

[prime egret]

It goes down by one every time we differentiate

[junior gale]

ok

[prime egret]

So for the nth derivative we have $(1-x)^{2016-n}$

[woven radish]

Pure

[prime egret]

Agreed?

[junior gale]

yea

when it tells us f^2016 (2016) is (2016) the x?

or that a new function?

[prime egret]

Yes

It’s the x

[junior gale]

so its now (1-2016)^2016?

so -2015?

[prime egret]

Why?

Oh you mean

f(2006)

But that’s not relevant here

[junior gale]

but the question asked that?

[prime egret]

it asks for $f^{(2006)} (2006)$

[woven radish]

Pure

[junior gale]

no look at the question

its 2016

[prime egret]

Alright

Point is it asks for the 2016th derivative of 2016

This has nothing to do with f(2016)

[junior gale]

ok

[prime egret]

Okay continue from here we now have $$(-1)^n \cdot (1-x)^n \cdot …$

[woven radish]

Pure
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[prime egret]

Now for the number term

For the first derivative we have

$2016$ which can be written as $\frac{2016!}{2015!}$

[woven radish]

Pure

[junior gale]

ok

[prime egret]

For the second derivative$2016 \cdot 2015 =\frac{2016!}{2014!}$

[woven radish]

Pure

[prime egret]

And the third $2016 \cdot 2015 \cdot 2014 = \frac{2016!}{2013!}$

[woven radish]

Pure

[prime egret]

We can therefore say that for the nth derivative we have $$\frac{2016!}{(2016-n)!}$$

[woven radish]

Pure

[prime egret]

And we got our expression for the nth derivative of f(x)

Plugging n=2016 into this formula yields 2016! which is the answer

[junior gale]

alright thanks

/close

[devout snow]

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[junior cradle]

a triangle ABC have A=30degrees, B=60degrees and AB = a

[junior cradle]

Find the length AC and BC expressed with a.

how do i solve this, have absoluttely no idea

[limber tangle]

30 60 90 is a special right triangle

[prime egret]

Right angle triangle

[junior cradle]

yep

[prime egret]

Do some trig

[junior cradle]

i have memorized the values but dont understand the whole express with ''a'' thing

[limber tangle]

answer in terms of a

[prime egret]

Draw a picture first

[prime egret]

Right now draw the abc

Triangle

The ratios between the sides would be the same

[junior cradle]

like this

they match and the last one, C must be 90 degrees

[prime egret]

Right so the hypothesuse is a

[junior cradle]

yes

[prime egret]

Let’s look at sinA

So sin30

We know this is 1/2

But we also know it’s CB/AB

$\frac{1}{2} = \frac{CB}{a}$

[woven radish]

Pure

[prime egret]

You following this so far?

[junior cradle]

yep

[prime egret]

Right so CB is a/2

Do the same thing for AC

You can consider cos30

[junior cradle]

ok let me try

sqrt3/2 / a then

[prime egret]

Yes which is sqrt3/2a

Wait

It’s $\frac{AC}{a} = \frac{\sqrt 3}{2}$

[woven radish]

Pure

[prime egret]

So AC = a sqrt3/2

[junior cradle]

ohh i think i understand now

prob have to read the chat one more time tho 🙂

thanks for the help

.close

[devout snow]

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[weak summit]

is this even true??

[weak summit]

this is equavalent to

this over R+-{0}

huuh?

any ideas

.close

[devout snow]

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[loud blade]

need help with basic trigonometric functions

[loud blade]

i need to simplify the circled problems

i got 3sin75°-2sin75° on this one

did i do it right or no

[vivid cliff]

aye aye

wassup

so

do u

have a

picture

of ur

work

it’s basically

using

addition formula

yk

[loud blade]

i dont

[loud blade]

ive slept through past 4 math classes and got a test tomorrow so im here studying at 11pm

[loud blade]

need to simplify not solve 😭

[vivid cliff]

this

is what I’m

talking about

[shadow fern]

Hmmmm

[vivid cliff]

aye?

does it

ring a bell

[loud blade]

aye i see it

[vivid cliff]

aye aye

nice

[loud blade]

first time seeing this shi

[vivid cliff]

ah alr

well

u learn

smth new

everyday

so

u know

ur special angles

30,45,60,90

[loud blade]

okay but like is this correct or no

[vivid cliff]

no

idk what u did

show me a picture

of ur work

[loud blade]

aight sec

i dont know what im doing

[vivid cliff]

aye

me neither

but

it’s okay

we learn

now

ye

alr so

look at

ur question

$3cos15 - 2sin75$

[woven radish]

Springsskateboard

[vivid cliff]

alr first

do u know

ur special angles

and stuff

[loud blade]

yes i think

[vivid cliff]

alr good

now

look at the cos

just the cos15

see the 15?

[loud blade]

15,30,45,60,75,90

right?

yes i do

i see the 15

[vivid cliff]

which 2 special angles subtracted give u

the 15

[vivid cliff]

no

[loud blade]

90-75

[vivid cliff]

15 isn’t one

[vivid cliff]

sure

any other pair

[loud blade]

60-45

[vivid cliff]

good

any other

[loud blade]

75-60

[vivid cliff]

75 isn’t a special

angle

[loud blade]

😭

[vivid cliff]

wait a min

[loud blade]

45-30

[vivid cliff]

lmao oops

[vivid cliff]

why did I say yes to that

I saw wrongly

75 isn’t

a special angle

[vivid cliff]

yep

[loud blade]

so its 30,60,90?

and 45

[vivid cliff]

so 60-45 or 45-30

gives u

15

[loud blade]

yes

[vivid cliff]

yep

so

u can use

either one

45-30

or 60-45

to replace

[loud blade]

okay...

[vivid cliff]

the 15 in the cos

so what do

u wanna choose

[loud blade]

lets do 60-45

[vivid cliff]

alr

nice

so

replace the

15

with that

and show me

what u got

[vivid cliff]

alr

u need

brackets

(60-45)

if it’s just

one number

then u don’t need

brackets

but here

[loud blade]

brackets added

[vivid cliff]

u have more than 1

[loud blade]

go on

[vivid cliff]

yep

good

alr

so

next

look at

our sin

sin75

[loud blade]

i have many sins

[vivid cliff]

what 2 special angles

added

[vivid cliff]

HAHAHA

[loud blade]

45+30

[vivid cliff]

yep

so replace

75 with that

aye aye nice

ure getting it

[loud blade]

since its -sin we gotta add special angles and because cos is positive we gotta subtract?

[vivid cliff]

nah it’s not like that

there’s no pattern

or anything

[loud blade]

ahh okay okay got it

[vivid cliff]

we just want 2 numbers

that add/subtract to the inside

yeye

so

what do u

have

[modest wigeon]

whats going on here bro

[vivid cliff]

nice

so

now

[modest wigeon]

where are you getting these silly values

[loud blade]

cat i told you the nice man is helping me shush

[vivid cliff]

u just needs

use this formula

[loud blade]

no comprendes

[modest wigeon]

isnt sin15 = cos75

equally distant from 0 or 90

[loud blade]

thats what i initially thought

[vivid cliff]

yeye

but I’m tryna

[topaz beacon]

It is

[vivid cliff]

make him see this

through that

[topaz beacon]

It might be easier with a unit circle visual

[vivid cliff]

because look at

[loud blade]

sooo i could have just gone straight forward with that instead of going through this process 😭

[vivid cliff]

the first work he did

oh wait

bruh

[loud blade]

im gonna cry

[vivid cliff]

u could’ve just done that

I’m so dumb

[loud blade]

i am confused, shaken, sobbing

[modest wigeon]

see bro this is why you listen to my made up formulas

[vivid cliff]

my bad bro

[loud blade]

so whats the answer

3sin75-2sin75?

[modest wigeon]

yea

[loud blade]

why u tell me it was wrong at first @vivid cliff 😭

[vivid cliff]

I didn’t realise 😭

eh issok

[loud blade]

what about this one

[vivid cliff]

I learnt from this too

[loud blade]

with tg and ctg

[modest wigeon]

same thing

[vivid cliff]

wait

[loud blade]

is it the same thing

[vivid cliff]

but this isn’t

simplified

[vivid cliff]

this

don’t they want

exact value

[loud blade]

my teacher wants us to just turn them into equal units or whatever

[vivid cliff]

it’s just sin75

[vivid cliff]

so exact or nah

[loud blade]

not exact

what i have is good i think

[vivid cliff]

oh alr then

[loud blade]

is it same process for tg and ctg

[modest wigeon]

yea bro

i told you 50 times

[loud blade]

alright i think im good for now

how to end help session

[modest wigeon]

.close

[loud blade]

.close

[devout snow]

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[maiden zinc]

an idea to integrate $\int \frac{dx}{cos(x)sin^2(x)}$?

[woven radish]

Max.cc

[maiden zinc]

i was thinking about posing u = cos(x) and du = -sin(x) dx
but i've some trouble to write the integral in function of u

[spare zealot]

<@&268886789983436800> this mariana user doesn't seem to be helping

[maiden zinc]

clearly not

[wooden zodiac]

csc^2xsecxdx

How can u write csc^2x also

[maiden zinc]

csc?

[wooden zodiac]

No

It's already written as cscxcscx=csc^2x

[devout snow]

@maiden zinc Has your question been resolved?

[maiden zinc]

bro what is that x)

<@&286206848099549185>

[forest depot]

1/sin^2(x)

That is csc^2(x)

[maiden zinc]

hum ok

and without that how can i solve that (because i haven't see that yet)

(too much that lol)

[devout snow]

@maiden zinc Has your question been resolved?

[devout snow]

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[stuck birch]

hello how can i start here?

[restive river]

you know how for every bilinear form, there is a corresponding matrix, such that:

$b(x, y) = x^T \cdot M \cdot y$

[woven radish]

rbit ✨

[stuck birch]

right

[restive river]

what is this matrix for the standard inner product?

[stuck birch]

the identity matrix?

[restive river]

yeah

[stuck birch]

yea but

should i do this with chain of equations?

[restive river]

i mean using that we can actually do it pretty directly:

$x^T \cdot A_{\beta} \cdot y = x^T \cdot \phi(y)$

[woven radish]

rbit ✨

[restive river]

wait whats the letter?

phi ok

instead of writing phi(y), what can we do instead?

[stuck birch]

A*y

[restive river]

right, so

$x^T \cdot A_{\beta} \cdot y = x^T \cdot A_{\phi} \cdot y$

[woven radish]

rbit ✨

[stuck birch]

wait so its just one line

i guess convert them to sum notation

[restive river]

yeah, a different approach to this instead would be to go through all the unit vector for x and y, and then using that to find the A phi matrix

and then linearity shows that this suffices

[stuck birch]

and then this proves uniqueness?

or do i still have to prove that

[restive river]

i think it does, because by plugging in all n² possible combinations of unit vectors for x and y, you get all n² elements of the matrix individually and then they have to be unique

but that takes a bit of work as you can guess, because then you also need to prove the matrix will do the job for all x and y

[stuck birch]

hmm ok

[restive river]

like you do
beta(e3, e4) = <e3, A*e4>
and then you get the A_34 entry of the matrix

[stuck birch]

right

hmm okay thank u

i hope this suffices

it does make sense

like $M_{\phi}$ is the only linear map possible for this

[woven radish]

b3s4d

[restive river]

yeah, matrices uniquely determine linear maps

[stuck birch]

okay

thanks for ur help

.close

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[fossil moth]

Sketch the graph of a function f with the following properties:
f is not continuous when x = 4 but limx→4 f(x) exists.
• f has a non-removable discontinuity when x = −2.
• f is increasing when x < −2.
• f is continuous at all points other than where x = −2 or x = 4.

[devout snow]

@fossil moth Has your question been resolved?

[devout snow]

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[clever dirge]

How do I solve this with squeeze theorem?

[clever dirge]

In particular the division is what im not sure what to do with

if it was 6hsin6h I would know how to solve it with -1 < sin6h < 1 and multiply 6 on each term

[tall knoll]

do you know instead how to evaluate $$\lim_{g \to 0} \frac {\sin(g)}{g}$$

[woven radish]

Steakanator

[clever dirge]

Guess not

[tall knoll]

really? that's usually the progression for such limit questions

[clever dirge]

if i cant substitute it I use limit properties right

I skipped a couple lessons on khan academy to get to squeeze theorem

[tall knoll]

that's perhaps why

the usual approach is to make the substitution g = 6h, which reduces to the limit I mentioned

[clever dirge]

On a calculator 0/0 is undefined but in this case it is 1, why is that?

sin(0) is 1 so perhaps that is why? but how did sin(g) become solo

[tall knoll]

because taking the limit is not the same as just evaluating a function at that point

the two happen to coincide if the function in question is continuous there (and that's indeed the definition of continuity at a point), but the two are different if there are discontinuities

and a denominator of x should be a good indicator that there's a discontinuity at 0

[devout snow]

@clever dirge Has your question been resolved?

[devout snow]

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[soft ginkgo]

Venn Diagrams - Geometrey

[bleak sun]

#❓how-to-get-help

[soft ginkgo]

i dont understand bruv

[bleak sun]

read #❓how-to-get-help

literally second bullet point

[soft ginkgo]

sorry mb

.close

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[restive river]

hi

[vivid cliff]

aye aye

wassup

so

hm

[restive river]

yo

[vivid cliff]

have u

tried anything

or nah

[restive river]

idk how to do it

[vivid cliff]

alr so

first thing

shortest distance

would be

a line

that includes P

that’s perpendicular

to the line u see

given to u

ye?

so first

u need to choose

any 2 points on the line

they gave u

and find the gradient/slope

then after that

u can find the gradient/slope

of the perpendicular line

by using

m1m2=-1

next

u needa find the c’s in both equation

then afterwards

find point of intersection

by making the 2 equations =

then solve for x

and get ur Y

then use distance formula

for the distance

[restive river]

the hell

[vivid cliff]

between the pt of intersection and P

and that’s it

[restive river]

im

confused

[hybrid snow]

What's the slope of the line

[restive river]

ok so

@hybrid snow @vivid cliff i finished it

can i tell me if im right

wait no i finished this *

[vivid cliff]

uh

no idts

[violet wind]

b^2=1 has two solution

[vivid cliff]

consider using distance formula

yeye

[devout snow]

@restive river Has your question been resolved?

[restive river]

@vivid cliff @violet wind

y= 1 or 3

is what i xan add to that

[violet wind]

Ye

[restive river]

@violet wind ok so

is this correct?

[vivid cliff]

idk

I can’t read

ur work

maybe u can

write on paper

and show

every step

[restive river]

uh

[restive river]

is the answer 8; -6

[devout snow]

@restive river Has your question been resolved?

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[kind mortar]

Are my examples & solution on solving quadratic equation by using the quadratic formula correct?

[pseudo basin]

your handwriting makes fives look like threes sometimes...

[kind mortar]

Yeah sorry 😦

But is there any problem with the example & solution?

[pseudo basin]

like, i would not read this as x=-5. it reads as x=-3

also i think you typoed in the equation you're solving in #3. did you mean 2x^2 + 5x - 3 = 0?

[kind mortar]

Yes

2x^2 +5x -3

[pseudo basin]

right, let's see

ok then #3 is correct

ok then handwriting issues aside all of these seem correct

[kind mortar]

Thanks

I'll rewrite them thank you very much for checking

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[red quartz]

I like remember but not really

[red quartz]

We were using some sort of number line method

I know we have to find what values make it 0 but how do I factor and simplify this

If I factor I think I should get it

I don’t know how to get the derivative I’m lost

[tall kernel]

I'd advise you to read up on the product and chain rules of derivatives.

[red quartz]

Because I know you multiply the exponent and subtract 1

I’m just lost with x-3^2

[tall kernel]

that's for the derivative of polynomials of functions yes.

[red quartz]

Yea but im trying to make it that no?

[tall kernel]

That's why I mentioned chain and product rules

[red quartz]

Mmmm ok

[tall kernel]

Think of it as a composite function

The inner function is x-3

[red quartz]

I don’t think I’ve learned that

That’s why

[tall kernel]

And the outer function is x^2

You're doing derivatives without understanding composite functions?

That's...unusual in Calculus

[red quartz]

I haven’t learned that term yet 🤷‍♂️

[tall kernel]

like uh

f[g(x)]

This

[red quartz]

I’ll ask my teacher tmr for sure about it

[tall kernel]

Yeah you need that concept

then chain rule

[red quartz]

Maybe I have

[tall kernel]

in order to differentiate (x-3)^2

[red quartz]

I’m kinda lost

I don’t know those terms

[tall kernel]

...yeah I dunno what your calculus course is doing if it doesn't teach this during differentiation

[red quartz]

Yea ima just skip it

And ask him tmr

[tall kernel]

[red quartz]

Thank you tho

.close

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[restive river]

why for this one do you have to do for part a, 68%+(95%-68%/2) = 81.5

%

then 1-(1-0.815)^2

why do you square for that part

and no idea for part b

[devout snow]

@restive river Has your question been resolved?

[devout snow]

@restive river Has your question been resolved?

[devout snow]

@restive river Has your question been resolved?

[devout snow]

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[warm lichen]

how does that become this

[rare mantle]

quadratic formula

[warm lichen]

thanks

your so big brain

.close

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[pseudo jacinth]

Find an example of two convergent sequences $(x_n)$ and $(y_n)$, where $x_n < y_n$ for all $n \in $\mathbb{N}$ , but \lim{} x_n \nless \lim{} y_n $

[woven radish]

m_g
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[pseudo jacinth]

anybody know this?

[balmy quest]

(n+1)/n and (n+2)/n

[pseudo jacinth]

Can you explain me why?

[balmy quest]

$$\lim_{n \to \infty}\frac{n+1}{n}=1=\lim_{n \to \infty}\frac{n+2}{n}$$

[woven radish]

秋水

[pseudo jacinth]

is (n+1)/n < (n+2)/n ?

[balmy quest]

yes, n+1<n+2

[pseudo jacinth]

and they are convergent?

[balmy quest]

yes, their limits are 1

[pseudo jacinth]

thank you!

[devout snow]

@pseudo jacinth Has your question been resolved?

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[hasty tide]

For f'(x) i used f(x)=ax^2+bx+c but now i need to use f''(x) should i use f(x)=ax^5+bx^4+cx^3+dx^2+ex+f or should i use something different
The new function needs to through -4 and 4

[patent tartan]

what was the original question

[hasty tide]

so g(x) and h(x) are 2 streets and for the first task i needed to find a new street function that connects -4 and 4 the street should be smooth and without a kink

for the first i used f(x) for smooth and f'(x) for no kink

[patent tartan]

whats a kink?

so you used a quadratic function/parabola for this then?

[hasty tide]

yes for the first task

and its kinda weird when i use a f''(x) for the quadratic function

[patent tartan]

what is the second task

[hasty tide]

To find a second function/street with f“(x)

[patent tartan]

just any function that connects -4 to 4?

[hasty tide]

The first function was -1/8x^2+2

[patent tartan]

or cant it be a quadratic now?

[hasty tide]

Well I need to know how to calculate it

[hasty tide]

I think it can but I also want to use a different way for it

[patent tartan]

okay say you use a cubic function

do you know that you can write polynomials as a product of linear factors?

the factors represent the roots

for example, x^2 + 3x + 2 = (x+1)(x+2) with roots at x = -1 and x = -2

[hasty tide]

so it means it goes through -1 and -2?

[patent tartan]

yes

a cubic function can be written as (x-a)(x-b)(x-c), we want two roots to be at -4 and +4

for example (x+4)(x-4)(x-c)

[hasty tide]

why did you use 4 to replace a and b?

[patent tartan]

a,b,c are the roots of the cubic function

in general

[hasty tide]

ohhh

[patent tartan]

the third root c can be anything really, we dont care about it now

but you want the function to be 4 at x=0 right?

[hasty tide]

Yes

[patent tartan]

lets say we pick this cubic function $(x-4)(x+4)(x-8)$ so the third root is at $x=8$, we can graph this

[woven radish]

nvx

[patent tartan]

,w plot (x-4)(x+4)(x-8)

[woven radish]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by Navix#0001

[hasty tide]

One question

How do you get the 8?

[patent tartan]

i just chose randomly

[hasty tide]

Can I pick any number?

[patent tartan]

if you do not have any other conditions for the function, then yes

or do you want there to be an extremal point at x=0?

[hasty tide]

What is a extremal point?

[patent tartan]

whats its called in english uhh, like where the tangent of the function is horizontal

,w plot x^2

[woven radish]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Navix#0001

[patent tartan]

like here the extremal point is at x=0

where the curvature is horizontal

[hasty tide]

Ohh yea I see it

There wasn’t any other conditions thank you

[patent tartan]

if you refer back to the previous graph we can see its not 4 at x=0

so we still need a little modification

[hasty tide]

You mean the height?

[patent tartan]

yea

its something like y=120 at x=0

[hasty tide]

yes its really high

[patent tartan]

we can tweak it a bit, remember we had
$$(x-4)(x+4)(x-8)$$

[woven radish]

nvx

[patent tartan]

we can multiply everything by a factor $a$ which doesnt change the roots
$$a(x-4)(x+4)(x-8)$$

[woven radish]

nvx

[hasty tide]

and now we need to find a? or pick a number

[patent tartan]

we now need to find $a$ such that $a(x-4)(x+4)(x-8) = 4$ if $x=0$

[woven radish]

nvx

[patent tartan]

can you solve this for $a$: $a(-4)(4)(-8) = 4$?